13,446 research outputs found
Universally Decodable Matrices for Distributed Matrix-Vector Multiplication
Coded computation is an emerging research area that leverages concepts from
erasure coding to mitigate the effect of stragglers (slow nodes) in distributed
computation clusters, especially for matrix computation problems. In this work,
we present a class of distributed matrix-vector multiplication schemes that are
based on codes in the Rosenbloom-Tsfasman metric and universally decodable
matrices. Our schemes take into account the inherent computation order within a
worker node. In particular, they allow us to effectively leverage partial
computations performed by stragglers (a feature that many prior works lack). An
additional main contribution of our work is a companion matrix-based embedding
of these codes that allows us to obtain sparse and numerically stable schemes
for the problem at hand. Experimental results confirm the effectiveness of our
techniques.Comment: 6 pages, 1 figur
Efficient, sparse representation of manifold distance matrices for classical scaling
Geodesic distance matrices can reveal shape properties that are largely
invariant to non-rigid deformations, and thus are often used to analyze and
represent 3-D shapes. However, these matrices grow quadratically with the
number of points. Thus for large point sets it is common to use a low-rank
approximation to the distance matrix, which fits in memory and can be
efficiently analyzed using methods such as multidimensional scaling (MDS). In
this paper we present a novel sparse method for efficiently representing
geodesic distance matrices using biharmonic interpolation. This method exploits
knowledge of the data manifold to learn a sparse interpolation operator that
approximates distances using a subset of points. We show that our method is 2x
faster and uses 20x less memory than current leading methods for solving MDS on
large point sets, with similar quality. This enables analyses of large point
sets that were previously infeasible.Comment: Conference CVPR 201
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